Question

Answer 1

1.

\(\sqrt{A}\le2\Rightarrow A\le4\)

\(\Rightarrow\dfrac{2\sqrt{x}+7}{\sqrt{x}+1}\le4\Rightarrow2\sqrt{x}+7\le4\sqrt{x}+4\) (do \(\sqrt{x}+1>0;\forall x\))

\(\Rightarrow2\sqrt{x}\ge3\Rightarrow\sqrt{x}\ge\dfrac{3}{2}\)

\(\Rightarrow x\ge\dfrac{9}{4}\)

2.

\(\sqrt{P}>3\Rightarrow\left\{{}\begin{matrix}P\ge0\\P>9\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}\sqrt{x}>1\\\dfrac{\sqrt{x}+1}{\sqrt{x}-1}>9\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}x>1\\\sqrt{x}+1>9\sqrt{x}-9\end{matrix}\right.\) (do \(x>1\Rightarrow\sqrt{x}-1>0\))

\(\Rightarrow\left\{{}\begin{matrix}x>1\\4\sqrt{x}< 5\end{matrix}\right.\) \(\Rightarrow1< x< \dfrac{25}{16}\)